Simulation of Rare Events in Lightwave Systems

这项提案中概述的工作的目标是开发基于蒙特卡洛的统计技术，以计算光通信系统中发生罕见事件(如比特丢失)的可能性。这些技术将适用于非常复杂的问题(例如，通过非线性和非自治项)，以至于在分析上难以解决，用于计算发生事件的概率，这些事件如此罕见，以至于无法使用标准计算方法进行量化。这些技术将依赖于使用微扰法和变分原理，结合最优化方法来降低基本偏微分方程组的维度，以确定合适的采样启发式。这项工作的直接应用将是确定当暴露于诸如放大器噪声等随机损伤时，调制格式对光纤通信线路的稳健性的影响。更广泛地说，光通信中的严格容限(每传输一个千兆比特或太比特就有一个丢弃比特)在行业中造成了大量问题，这些技术将很好地适应这些问题。最后，在工业和自然界中出现的许多情况下，人们想要确定在随机非线性波背景下发生罕见事件的概率；这项工作将提供实现这一点的技术。该GOALI项目由数学科学处(DMS)和重大计划署多学科活动办公室(OMA)共同资助。

The goal of the work outlined in this proposal is to develop Monte Carlo-based statistical techniques to calculate the likelihood of rare events such as dropped bits in optical communications systems. These techniques will be applicable to problems that are so complex (through nonlinear and nonautonomous terms, for example) as to be analytically intractable, for calculating the probability of events that are so rare as to be impossible to quantify using standard computational methods. The techniques will rely on using perturbation methods and variational principles, in conjunction with optimization methods, to reduce the dimension of the underlying partial differential equations in order to determine appropriate sampling heuristics.The immediate application of this work will be to determine the impact of modulation formats on the robustness of a fiber-optic communications line when exposed to random impairments such as amplifier noise. More broadly, the strict tolerances in optical communications (a single dropped bit for each gigabit or terabit transmitted) provide for a large host of problems in the industry to which these techniques will be well suited. Finally, there are many situations that arise in industry and nature where one would liketo determine the probability of a rare event in the context of a stochastic nonlinear wave setting; this work will provide techniques to accomplish this. This GOALI project was jointly funded by the Division of Mathematical Sciences (DMS) and the MPS Office of Multidisciplinary Activities (OMA).